November 2018 - mathfun@mailman.xmission.com

Re: [math-fun] The moving now (was: Messages in pi)
by Dan Asimov 10 Dec '18

10 Dec '18

Thoughts about what Mike wrote below: 1. I don't know about this arrow of time. I haven't kept up to date, but isn't there a theorem that if you reverse charge, parity, and time, any movie of something physically possible would still be possible if run backward? (And if charge and parity are not involved, then you can just run the same movie backward without change.) Of course, in our neighborhood of spacetime, we are living in a part of the universe where stars radiate energy in the positive direction of time (t+). Given that fact, things like eggs breaking in t+ but seemingly never reassembling follow from the existence of evolution. But in principle if we could imagine where the recent past of [all spacetime that could affect our present] is being copied — in a CPT-reversed way, at least T — presumably the same past would unfold just like our own future. But Mike himself pointed out that "entropy increases" isn't by itself a fully adequate explanation. 2. Mike asks "More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously?" My first answer is, It sure *feels* as if the recent past is something that I lived very recently. And the recenter the past, the recenter it feels. It's enough to make one want to locate one's focus in a new place, to recenter oneself. *Maybe* it's just a coincidence that all these moments fit together into a continuous narrative. It feels much more likely that something crucial about how the moments came into being is real-numbery, i.e., somehow 1-dimensional. I think the real numbers R can be characterized as the only connected topological space such that the removal of any point leaves just two connected components. But there may be another condition like, y'know, Hausdorffness or local compactness or homogeneity, that I'd rather not mention, necessary for this uniqueness. But: Would we indeed feel as we in fact do, if all phases of our lives were being lived, kind of, "at the same time" ? Who is feeling all those other moments that we lived or will live? (Not 100% serious, but still.) —Dan "All you have is the state of your brain at that given point in time." I think. —Dan ----- On Wed, Nov 28, 2018 at 1:47 PM Dan Asimov <dasimov(a)earthlink.net> wrote: > > That's probably my preferred view, but there are problems reconciling it with > everyday experience. It would mean that all ages t of (say) me are living their > lives equally, in some sense of equally. > > But how does that explain the experience we have of living our lives in the order > of the real numbers, and the fact that it keeps getting later? A too-cute answer is, "Because the arrow of time points in the direction of increasing entropy." More carefully, how could you distinguish the experience of living the events out of order from living them in order, or from living them simultaneously? All you have is the state of your brain at that given point in time. -----

6 5

[math-fun] The moving now (was: Messages in pi)
by Dan Asimov 01 Dec '18

01 Dec '18

That's probably my preferred view, but there are problems reconciling it with everyday experience. It would mean that all ages t of (say) me are living their lives equally, in some sense of equally. But how does that explain the experience we have of living our lives in the order of the real numbers, and the fact that it keeps getting later? —Dan Mike Stay writes: ----- Just as [I wrote] below: > Another possibility is that our lives are being lived from start to finish, > unchangingly. The parts we have already lived as well as the parts we have > yet to live, just like the present moment, all entirely as equals. This > just leaves unexplained how we can then experience a moment as separate from > other moments. I don't see what the problem is. Plug in t, get the experience at t. -----

5 4

Re: [math-fun] fair Carlsen vs Stockfish comparison
by Dan Asimov 30 Nov '18

30 Nov '18

I'd like to use this thread to say I don't like the modern championship chess match with its rules like: A tied score at the end of N games means: * the current champion keeps the title, or * there are a series of playoffs of what is arguably a different game, as well as for a duration so short that for two closely matched players the end result could be no better than flipping a coin. I vote for a return to the days when the winner had to reach a certain number of wins, by some margin (two games?) and they damn well kept playing until someone won. And eventually someone did win. What's the matter with that? If those were the rules, it's doubtful either player would want to tire themselves out with an unduly long series of draws. (Though a few draws for the purpose of scoping out the other player's tricks might help.) —Dan

3 2

[math-fun] fair Carlsen vs Stockfish comparison
by Veit Elser 29 Nov '18

29 Nov '18

How do Carlsen and a laptop running Stockfish compare, when power consumption is used to level the playing field? Both the brain and a laptop use roughly 20W, but while most of that 20W can go toward computing the best move on the laptop (dimmed display, etc.), my guess is that only a small fraction of that is used by the brain for the same task (we can’t shut down all those processes required to keep us alive). Does anyone have an estimate of “higher-order brain function” energy consumption, and whether Stockfish would still be competitive with *that* energy budget? -Veit

2 1

[math-fun] It would take five Ramanujans to impeach Trump
by Bill Gosper 29 Nov '18

29 Nov '18

In[845]:= 5*1729 Out[845]= 8645 —rwg

3 2

Re: [math-fun] Mathematics of SETI protocols ?
by Keith F. Lynch 29 Nov '18

29 Nov '18

Henry Baker <hbaker1(a)pipeline.com> wrote: > Tom Knight wrote: >> I've always wondered why we think messages have to happen at time >> scales similar to ours. >> Why couldn't a perfectly plausible alien civilization send messages >> at the rate of a bit per year, or a bit per century? >> We have a very narrow view of what "short" or "long" time periods are. > Perhaps some aliens have been trying to communicate with use via ice > ages -- e.g., 20,000 years per symbol -- or via sunspot cycles, and > we just haven't been paying attention? It seems unlikely that aliens who work that slowly would have had time to evolve already, given that the universe is only 13.8 billion years old. Of course they could send slowly even if it's not natural to them. QRSS (as radio amateurs call it) is a great way to send signals long distances with low powers. The slowest I've heard of is one bit per hour. A QRSS signal was successfully bounced off the moon despite having an absurdly low transmitter power of three milliwatts. Might aliens send quickly? Sure. Indeed, our 100 gigabit per second Ethernet would seem utterly inhuman to 19th century telegraphers, who averaged about 10 bits per second. A telegrapher patiently tapping away non-stop from the invention of the telegraph until the present would send less than a 100 gigabit Ethernet would send in a second. It would be possible to send at several speeds at once -- a self- similar fractal signal. If you're a real speed freak, see the YouTube video "Timelapse of the entire universe." 13.8 billion years compressed into 10 minutes. On that scale, dinosaurs evolved ten seconds ago and went extinct three seconds ago, the continents drift at hypersonic speeds, and civilization began less than half a millisecond ago.

2 1

Re: [math-fun] Messages in pi
by Dan Asimov 28 Nov '18

28 Nov '18

----- ... there is a sense of “now” that runs unidirectionally into the future ... ----- This phenomenon has fascinated me for a while now. Consider the experience that everyone has of the flow of time, specifically "the moving now" Now it's now, but now it's a little later and now it's later yet. Pedestrian, yet no one knows how to model what happening so that physics, mathematics, and our own experience don't seem to contradict each other. Like, take the spacetime view of physics, where it all exists at once. But wait — how does that jibe with our experience of our lives as a succession of instants ordered like the real numbers? OK, maybe our consciousness is like the lit end of a fuse, moving along our worldline in 4-space? But if so, this motion seems to assume another kind of "time" through which it happens. So what gives? Another possibility is that our lives are being lived from start to finish, unchangingly. The parts we have already lived as well as the parts we have yet to live, just like the present moment, all entirely as equals. This just leaves unexplained how we can then experience a moment as separate from other moments. So: paradox. —Dan Veit Elser wrote: ----- > On Nov 28, 2018, at 11:31 AM, James Propp <jamespropp(a)gmail.com> wrote: > > Julia Robinson has a good quote: "What is proved about numbers will be a > fact in any universe.” This still suffers from the bias that “intelligent life” runs on a platform that is “open” in the sense of physics, where there is a sense of “now” that runs unidirectionally into the future. For example, if some form of life was effectively a closed system, with perfect symmetry under time reversal (i.e. unitary evolution), I very much doubt that questions involving the operations of arithmetic or logic, most of which are not reversible, would arise (be considered interesting). The only work of fiction I know of that brings up this bias is Vonnegut’s Slaughterhouse Five, in which the Tralfamadorians have managed to become “unstuck in time”, that is, they experience the events on their world-lines not in sequence but as a single entity. We have the means, in principle, to build new kinds of AIs that are not subject to this bias. Whether there is anything interesting to talk about with them, or whether there is even a sense in which we could carry on a conversation, is another question. -----

2 1

Re: [math-fun] Bosons v Fermions in Quantum Computation ?
by Henry Baker 28 Nov '18

28 Nov '18

Thanks, Mike. Yes, I ran across anyons in my Google searching, so I'll have do some reading up on them. Tim Byrnes also looks like an interesting fellow, so I'll check out his papers. BTW, I forgot to mention that among their other features, photons can exhibit quantum features at *room temperature* -- e.g., polarization, beam splitting & combining, interference, etc. (Well, at least room temperature defined by standard thermometers.) Also, BTW, pure *photon gasses* look like an interesting & elegant model, though perhaps not (yet?) for QC. I wonder if they can be "bottled" within an optical fiber... I'm going to try to find a version of Carnot's Engine using a photon gas as its working fluid. At 09:05 PM 11/27/2018, Mike Stay wrote: >http://nyu.timbyrnes.net/research/quantum-information-using-bose-einstein-c… > >There's a third option in two dimensions, the anyon. One promising >model of quantum computation involves braided anyons, since relatively >large perturbations won't change the braiding. >https://en.wikipedia.org/wiki/Anyon#Non-abelian_anyons > >On Tue, Nov 27, 2018 at 8:42 PM Henry Baker <hbaker1(a)pipeline.com> wrote: >> Is it just me, or does anyone else think that *bosons* >> are a better choice for Quantum Computation than >> *fermions* ? >> >> With bosons, a QC engineer has the option of putting >> a large number of bosons (i.e., a large amount of energy) >> into every state, while with Fermions, you're dealing with >> a single, quite small amount of energy state. Not a lot >> of design space to work with. >> >> We've also got lots and lots of experience with electrical >> and magnetic fields and electromagnetic photons. >> >> Yes, photons are "large" compared with the feature sizes >> enabled by electrons, but on the other hand, we're now >> approaching the ~ 1 nmeter size needed for quantum dots >> for visible light photons. >> >> What am I missing here? > >-- >Mike Stay - metaweta(a)gmail.com >http://math.ucr.edu/~mike >https://reperiendi.wordpress.com

2 1

[math-fun] Bosons v Fermions in Quantum Computation ?
by Henry Baker 28 Nov '18

28 Nov '18

Is it just me, or does anyone else think that *bosons* are a better choice for Quantum Computation than *fermions* ? With bosons, a QC engineer has the option of putting a large number of bosons (i.e., a large amount of energy) into every state, while with Fermions, you're dealing with a single, quite small amount of energy state. Not a lot of design space to work with. We've also got lots and lots of experience with electrical and magnetic fields and electromagnetic photons. Yes, photons are "large" compared with the feature sizes enabled by electrons, but on the other hand, we're now approaching the ~ 1 nmeter size needed for quantum dots for visible light photons. What am I missing here?

2 1

[math-fun] "The twenty five fourthsth and sesquith singular values", typeset
by Bill Gosper 27 Nov '18

27 Nov '18

Mystery: Mathworld: Elliptic Integral Singular Value When the elliptic modulus <http://mathworld.wolfram.com/EllipticModulus.html> [image: k] has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions <http://mathworld.wolfram.com/GammaFunction.html>. Abel (quoted in Whittaker and Watson 1990, p. 525) proved that whenever K(1-k)/K(k) = (a + b√n)/(c + d√n) [parameter notation], where [image: a], [image: b], [image: c], [image: d], and [image: n] are integers <http://mathworld.wolfram.com/Integer.html>, [image: K(k)] is a complete elliptic integral of the first kind <http://mathworld.wolfram.com/CompleteEllipticIntegraloftheFirstKind.html>, then the elliptic modulus <http://mathworld.wolfram.com/EllipticModulus.html> [image: k] is the root <http://mathworld.wolfram.com/Root.html> of an algebraic equation with integer <http://mathworld.wolfram.com/Integer.html> coefficients <http://mathworld.wolfram.com/Coefficient.html>. (i.e., it's an algebraic number?) I can't make this work, except for a=c=0, and n rational, where it always works. E.g., no dice for K'/K = golden ratio. Who spazzed: Abel, W&W, eww, or me? Anyway here are two carefully simplified cases. n = 25/4 from yesterday: gosper.org/K÷K=2÷5.pdf <http://gosper.org/K÷K=2÷5.pdf>and n = 3/2: gosper.org/sesquith.pdf . Does anyone know why we fuss over the nth singular value when n can apparently be any rational? —rwg

1 1